December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills. December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 20 Aug 2015
Posts: 390
Location: India

A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
09 Feb 2016, 12:02
Question Stats:
66% (02:17) correct 34% (02:32) wrong based on 152 sessions
HideShow timer Statistics
A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue? A. 15/56 B. 41/56 C. 13/28 D. 15/28 E. 5/14
Official Answer and Stats are available only to registered users. Register/ Login.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8656
Location: Pune, India

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
09 Feb 2016, 22:13
TeamGMATIFY wrote: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?
A. 15/56 B. 41/56 C. 13/28 D. 15/28 E. 5/14 The probability of selecting 6 and leaving 2 such that 1 is white and the other blue is the same as the probability of selecting 2 such that one is white and the other blue while 6 are remaining. Probability of picking first blue and then white = (3/8)*(5/7) Probability of picking first white and then blue = (5/8)*(3/7) Total probability = (3/8)*(5/7) + (5/8)*(3/7) = 15/28 Answer (D)
_________________
[b]Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
09 Feb 2016, 18:26
TeamGMATIFY wrote: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?
A. 15/56 B. 41/56 C. 13/28 D. 15/28 E. 5/14 Good question. +1 The required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer.




Math Expert
Joined: 02 Aug 2009
Posts: 7098

A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
10 Feb 2016, 00:38
TeamGMATIFY wrote: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?
A. 15/56 B. 41/56 C. 13/28 D. 15/28 E. 5/14 Hi, another way to look at the problem..what is the way to have 1 of Blue and 1 of white in the last two remaining.. it is to pick only 2 BLUE in the first 6 pickedWAYs to have 2 BLUE in the 6 picked = 6C2= 15.. what are total ways to pick 6 out of 8 = 8C6= 28.. The prob = 15/28 D
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Intern
Joined: 09 Feb 2016
Posts: 5

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
10 Feb 2016, 04:26
VeritasPrepKarishma wrote: The probability of selecting 6 and leaving 2 such that 1 is white and the other blue is the same as the probability of selecting 2 such that one is white and the other blue while 6 are remaining. Hello VeritasPrepKarishma, can you explain how this is the same.



CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
10 Feb 2016, 06:32
PavaniRaghunath wrote: VeritasPrepKarishma wrote: The probability of selecting 6 and leaving 2 such that 1 is white and the other blue is the same as the probability of selecting 2 such that one is white and the other blue while 6 are remaining. Hello VeritasPrepKarishma, can you explain how this is the same. It is true because the total number of balls of both the colors does not change. It does not matter whether you reach 1 white ball at the end by removing 4 white before or you remove 1 white to have 4 white remaining. In simpler terms , Ill use the example fo the white balls: you end up getting the same answer whether you do 1+4 or 4+1. If you remove 1 w and 1 b ball at the start, the probability = (5C1*3C1)/8C6 If you remove 1 w and 1 b ball at the end, the probability = (5C4*3C2)/8C6 Both these equations give the same value as 5C1 = 5C4 and 3C1 = 3C2 Hope this helps.



Intern
Joined: 10 Jul 2014
Posts: 3
Concentration: Finance, Strategy

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
10 Feb 2016, 07:38
Honestly the easiest way to solve this is to draw it out and eyeball it.
B B B W W W W W
Visually, you can see that there are 15 combinations of one blue marble and one white marble (the first "B" combined with all 5 "W" + the second "B" combined with all 5 "W" + the third "B" combined with all 5 "W" = 15).
Then just use the combination formula for 8C2 to find the total number of combinations.
8!/2!*6! = 8*7/2 = 28
Answer is thus 15/28



Intern
Joined: 09 Feb 2016
Posts: 5

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
10 Feb 2016, 08:32
Engr2012 wrote: It is true because the total number of balls of both the colors does not change. It does not matter whether you reach 1 white ball at the end by removing 4 white before or you remove 1 white to have 4 white remaining. ok thanks. Looks like my quant concepts are quite rusty. Long way ahead...looks like .



Senior Manager
Joined: 20 Aug 2015
Posts: 390
Location: India

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
10 Feb 2016, 12:57
PavaniRaghunath wrote: VeritasPrepKarishma wrote: The probability of selecting 6 and leaving 2 such that 1 is white and the other blue is the same as the probability of selecting 2 such that one is white and the other blue while 6 are remaining. Hello VeritasPrepKarishma, can you explain how this is the same. Let us try to make this simpler. If the question had instead asked: "A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only ONE is left in the bag. What is the probability that it is blue?" We can say that there are two equivalent ways of going about this: 1. We take out 7 marbles and leave one in the bag. 2. We take out one and leave 7 in the bag. These two operations are equivalent. After all, we are randomly separating one marble from the other seven. Hence, these two experiments will yield the same probability. You can now extend this to the case where 2 marbles need to be separated from the rest.



Intern
Joined: 10 Feb 2016
Posts: 8
WE: Sales (Consulting)

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
10 Feb 2016, 15:39
Ways to select out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D SHOULD BE THE ANSWER , PLEASE GIVE KUDOS, IF U LIKE .THANKS



Board of Directors
Joined: 17 Jul 2014
Posts: 2621
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
09 Apr 2016, 18:18
oh damn...can't believe I missed this one... overcomplicated myself... 8C6=28 5C4 * 3C2 = 5x3 = 15 15/28 damn...



Manager
Joined: 01 Mar 2014
Posts: 116

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
19 Apr 2016, 09:51
Engr2012 wrote: TeamGMATIFY wrote: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?
A. 15/56 B. 41/56 C. 13/28 D. 15/28 E. 5/14 Good question. +1 The required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. Really like this approach. Just one question  do we consider the number of ways of choosing the balls? How can we decide when to do that? Please suggest.! Thank you!!



Intern
Joined: 27 Mar 2016
Posts: 2

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
19 Apr 2016, 10:29
Another quick solution:
Prob. that 1B & 1W remains in the bag = (Number of ways we can select 6 balls 2B & 4W  from the Bag) / (Total number of ways we can choose 6 balls from the bag)
Numerator = 6P6 / (2!*4!) = 15 Denominator = 8C6 = 28 Required prob. = 15/28
Thanks.



CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
19 Apr 2016, 15:16
MeghaP wrote: Engr2012 wrote: TeamGMATIFY wrote: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?
A. 15/56 B. 41/56 C. 13/28 D. 15/28 E. 5/14 Good question. +1 The required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. D is thus the correct answer. Really like this approach. Just one question  do we consider the number of ways of choosing the balls? How can we decide when to do that? Please suggest.! Thank you!! What do you mean by "do we consider the number of ways of choosing the balls", are you referring to the very process of choosing lets say 6 out of 8 balls or something else? Or is your question more about when to use the order of selection of balls (permutation vs combination)?



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4277
Location: United States (CA)

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
28 Jun 2017, 16:00
TeamGMATIFY wrote: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?
A. 15/56 B. 41/56 C. 13/28 D. 15/28 E. 5/14 We need to determine the probability of selecting 2 blue marbles and 4 white marbles in 6 selections. The number of ways to select the blue marbles is 3C2 = 3 and the number of ways to select the white marbles is 5C4 = 5. Thus, the total number of ways is 3 x 5 = 15. The total number of ways to select 6 marbles from 8 is 8C6 = (8 x 7 x 6 x 5 x 4 x 3)/6! = (8 x 7 x 6 x 5 x 4 x 3)/(6 x 5 x 4 x 3 x 2) = (8 x 7)/2 = 28. Thus, the probability is 15/28. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 10 May 2015
Posts: 1

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
29 Jun 2017, 02:15
TeamGMATIFY wrote: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability that out of the two, one is white and one is blue?
A. 15/56 B. 41/56 C. 13/28 D. 15/28 E. 5/14 There are two marbles remaining (one white and one blue). In other words, 2 blue marbles out of 3 and 4 white marbles out of 5 are remaining. Ways to select 2 blue marbles: 3c2 Ways to select 4 white marbles: 5c4 Total ways to select is to select 6 marbles out of 8 i.e. 8c6 Probability: 3c2*5c4/8c6= 15/28



Manager
Joined: 30 Mar 2017
Posts: 135

Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra
[#permalink]
Show Tags
30 Jul 2018, 17:09
Another way to think of it...
If you arrange the 3 blue and 5 white in a row, how many of those arrangements end in BLUEWHITE or WHITEBLUE?
Total # of arrangements of 3 blue, 5 white: 8!/3!5! = 56 # of arrangements ending in BW or WB = (arrange 2 blue and 4 white) * 2 = (6!/2!4!) * 2 = 30
So, 30/56 (15/28) ways to arrange 3 blue and 5 white in a row such that the last 2 marbles are BW or WB.
Answer: D




Re: A bag contains 3 blue and 5 white marbles. One by one, marbles are dra &nbs
[#permalink]
30 Jul 2018, 17:09






